Method for Measuring SOC of a Battery in a Battery Management System and the Apparatus Thereof

ABSTRACT

According to an embodiment of this invention, a method for measuring SOC (State Of Charge) of a battery comprises the steps of: obtaining current data, voltage data and temperature by measuring the current, the voltage and the temperature of a battery; calculating SOCi (State Of Charge based on current) by accumulating the current data; calculating open circuit voltage by using an equivalent circuit model which simply presents the current data, the voltage data and the battery through an electric circuit; calculating SOCv (State Of Charge based on voltage) by using the temperature data and the open circuit voltage; and choosing at least one of the SOCi and the SOCv as SOC of the battery by using the SOCi and the SOCv based on the judgment on the current state of the battery for a certain time interval.

TECHNICAL FIELD

The present invention relates to a method for measuring SOC (State OfCharge) of a battery in a battery management system and an apparatusthereof, and more particularly, to a method for setting up SOCi (StateOf Charge based on current) or SOCv (State Of Charge based on voltage)to SOC of a battery in a battery management system according to adesired condition using a simple equivalent circuit, and an apparatusthereof.

BACKGROUND ART

An automobile with an internal combustion engine using gasoline or heavyoil generally has a serious influence on the generation of pollutionlike atmospheric pollution. Therefore, in order to reduce the generationof pollution, there have been many efforts to develop a hybrid vehicleor an electric vehicle.

Recently, there has developed a high power secondary battery using ahigh energy density non-aqueous electrolyte. The high power secondarybattery may be provided in plural and connected in series in order toform a high capacity secondary battery.

As described above, the high capacity secondary battery (hereinafter,called “battery”) is typically comprised of the plurality of secondarybatteries connected in series. In case of the battery, particularly, anHEV battery, since a few or a few ten secondary batteries arealternately charged and discharged, there is a necessity of managing thebattery to control the charging and discharging of the battery andmaintain the battery in an appropriate operation state.

To this end, there is provided BMS (Battery Management System) formanaging all the states of the battery. The BMS detects voltage,current, temperature or the like, estimates SOC through a calculatingoperation and controls the SOC so as to optimize the fuel consumptionefficiency of a vehicle. In order to precisely control the SOC, it isnecessary to exactly measure the SOC of the battery in the charging anddischarging operations are carried out.

As a prior art, there is disclosed Korean Patent Application No.2005-00611234 (filed on Jul. 7, 2005) entitled “Method for resetting SOCof secondary battery module”.

In order to precisely calculate the SOC of the battery, theabove-mentioned prior art includes measuring a current value, a voltagevalue and a temperature vale of a battery module when turning on aswitch, calculating initial SOC using the measured values, accumulatingthe current value, calculating actual SOC according to the accumulatedcurrent value, determining whether the battery module is in a no-loadstate, determining whether the actual SOC is within a setup range thatcan be measured by accumulating the current value if the battery moduleis in the no-load state, and calculating the SOC according to thevoltage value by measuring the voltage value if the actual SOC isoutside the setup range. However, the prior art does not disclose amethod that applies a simple equivalent circuit to an actual battery andan apparatus thereof.

Generally, SOCi does not have errors in the short term, but, as shown inFIG. 1, there is a tendency that the errors are accumulated. Therefore,in case that the battery is operated for a long time, considerable erroris occurred. Especially, the accumulative error is mostly generated whenthe charging or discharging of battery is completely achieved. This iscaused by that the degree of precision is influenced by the errorsoccurred by reduction of SOC due to self-discharge, and omission of LBSdigit of CPU for calculating the SOC. Further, since the precisiondegree of the SOC is largely dependent on a current measuring sensor, itis impossible to correct the errors when the sensor has a trouble.

However, as shown in FIG. 2, SOCv measures the SOC through an opencircuit voltage. In this measuring method, it is possible to obtain veryprecise results when a current is not flowed. However, when the currentis flowed, the precision degree of the SOCv is dependent on a chargingand discharging pattern of a battery. Therefore, since the precisiondegree of the SOC is also dependent on the charging and dischargingpattern, it is deteriorated. Furthermore, the charging and dischargingpattern that deteriorates the precision degree of the SOCv is within arange that a typical battery is used. Thus, although only the SOCv isused, there is also a problem that has to accept the considerable error.

DISCLOSURE Technical Problem

An object of the present invention is to provide a method for measuringSOC (State Of Charge) of a battery in a battery management system and anapparatus thereof, which uses a simple equivalent circuit model and anadaptive digital filter and thereby easily and precisely measure the SOCof the battery.

Another object of the present invention is to provide a method formeasuring SOC (State Of Charge) of a battery in a battery managementsystem and an apparatus thereof, which determines whether a low currentstate is maintained for a desired time period and then sets up SOCi(State Of Charge based on current) or SOCv (State Of Charge based onvoltage) to SOC of the battery, thereby easily and precisely measuringthe SOC of the battery.

Technical Solution

To achieve the object of the present invention, the present inventionprovides a method for measuring SOC of a battery, comprising obtainingcurrent data, voltage data and temperature data by measuring current,voltage and temperature of the battery; calculating SOCi (State OfCharge based on current) by accumulating the current data; calculatingOCV (Open Circuit Voltage) using an equivalent circuit model in whichthe current data, the voltage data and the battery are simply expressedby an electric circuit; calculating SOCv (State Of Charge based onvoltage) using the temperature data and the OCV; and judging a currentstate of the battery for a desired period of time, and setting up theSOC of the battery using at least one of the SOCv and the SOCi.

Further, the present invention provides an apparatus for measuring SOCof a battery, comprising a battery information obtaining part thatmeasures current, voltage and temperature of the battery and obtainscurrent data, voltage data and temperature data; a current accumulatingpart that calculates SOCi by accumulating the current data; a OCVcalculating part that calculates OCV using an equivalent circuit modelin which the current data, the voltage data and the battery are simplyexpressed by an electric circuit; a SOCv estimating part that estimatesSOCv using the temperature data and the OCV; and a SOC setting part thatjudges a current state of the battery for a desired period of time, andsets up the SOC of the battery using at least one of the SOCv and theSOCi.

ADVANTAGEOUS EFFECTS

The present invention easily and precisely measures the SOC of thebattery by using the simple equivalent circuit model and the adaptivedigital filter.

Further, the present invention determines whether the low current stateis maintained for a desired time period and then sets up the SOC of thebattery using at least one of the SOCi and the SOCv, thereby easily andprecisely measuring the SOC of the battery.

DESCRIPTION OF DRAWINGS

The above and other objects, features and advantages of the presentinvention will become apparent from the following description ofpreferred embodiments given in conjunction with the accompanyingdrawings, in which:

FIG. 1 is a graph showing a case that SOC of a battery is set up byusing conventional SOCi.

FIG. 2 is a schematic view showing a case that the SOC of the battery isset up by using conventional SOCv.

FIG. 3 is a block diagram of an apparatus for measuring SOC of a batteryin accordance with an embodiment of the present invention.

FIG. 4 is a flow chart of a method for measuring the SOC of the batteryin accordance with an embodiment of the present invention.

FIG. 5 is a graph shown a result of simulation in a case that offset of1A occurs in accordance with an embodiment of the present invention.

FIG. 6 is a view showing an equivalent circuit model in accordance withan embodiment of the present invention.

FIG. 7 is a graph showing actual SOC and calculated BMS SOC in case ofusing a model providing an integration effect in accordance with anembodiment of the present invention.

FIG. 8 is a graph showing a compensation point in case of using themodel providing the integration effect in accordance with an embodimentof the present invention.

FIG. 9 is a view showing an equivalent circuit model in accordance withanother embodiment of the present invention.

FIG. 10 is a graph showing a proposed time criteria in accordance withan embodiment of the present invention.

FIG. 11 is a graph showing an error in case of performing a simulationwith a time criteria of 20 seconds and the proposed time criteria inaccordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF MAIN ELEMENTS

-   -   100: current accumulating part    -   200: low pass filtering part    -   300: open circuit voltage calculating part    -   400: SOCv estimating part    -   500: SOC setting part

BEST MODE

Various terms used in the application are generally described in thisfield, but in a special case, some terms are optionally selected by theapplicant. In this case, the meanings thereof are defined in thedescription of the present invention. Therefore, the invention should beunderstood with the meanings of the terms, but not names thereof.

Hereinafter, the embodiments of the present invention will be describedin detail with reference to accompanying drawings.

FIG. 3 is a block diagram of an apparatus for measuring SOC of a batteryin a battery management system in accordance with an embodiment of thepresent invention. Referring to FIG. 3, the apparatus for measuring SOCof a battery includes a battery information obtaining part (not shown),a current accumulating part 100, a low pass filtering part 200, an opencircuit voltage calculating part 300, a SOCv estimating part 400 and aSOC setting part 500.

A process for calculating the SOC of a battery in the battery managementsystem (hereinafter, called “BMS SOC”) includes six steps as follows:

First step: collection of current and voltage data

Second step: calculation of SOCi through current accumulation

Third step: low pass filtering

Fourth step: equivalent circuit model and adaptive digital filtering

Fifth step: calculation of SOCv through open circuit voltage andtemperature

Sixth step: proper selection of SOC.

The battery information obtaining part carries out the first step. Thatis, the battery information obtaining part collects current data,voltage data, temperature data and the like from the battery managementsystem (BMS). The collected current data is transferred to the currentaccumulating part 100. In the current accumulating part 100, the currentdata is accumulated and then added to SOC (SOC(k−1) in FIG. 3)calculated in the previous time interval, thereby calculating SOCi.

Further, the current data and the voltage data collected by the batteryinformation obtaining part are transferred to the low pass filteringpart 200. The low pass filtering part 200 filters the current data andthe voltage data and then transfers them to the open circuit voltagecalculating part 300. The open circuit voltage calculating part 300calculates parameters used in the equivalent circuit model through theequivalent circuit model and an adaptive digital filtering, and thencalculates open circuit voltage (OCV) using the parameters. The SOCvestimating part 400 estimates SOCv using the temperature data and theOCV, and then transfers the estimated SOCv to the SOC setting part 500.The SOC setting part 500 sets up the SOCi calculated in the currentaccumulating part 100 or the SOCv estimated in the SOCv estimating part400 to the BMS SOC according to a predetermined criteria. The detailedprocess performed in each part of the SOC measuring apparatus will bedescribed below with reference to FIGS. 5 to 10.

FIG. 4 is a flow chart of a method for measuring the SOC of the batteryin accordance with an embodiment of the present invention. The SOCmeasuring method will be described using the SOC measuring apparatus inFIG. 3.

Referring to FIG. 4, the battery information obtaining part measures thecurrent data, the voltage data, the temperature data and the like of abattery pack in real time from the BMS (S401). And the currentaccumulating part 100 accumulates the current data and calculates theSOCi (S402). Then, the low pass filtering part 200 filters the currentdata and the voltage data (S403).

The filtered current data and voltage data are transferred to the OCVcalculating part 300, and the OCV calculating part 300 calculates theparameters used in the equivalent circuit model through the adaptivedigital filtering (S404) and calculates the OCV Vo using the parameters(S405). And the SOCv estimating part 400 estimates the SOCv using theOCV (S406).

Then, the SOC setting part 500 determines whether a low current state ismaintained. If the low current state is maintained (S407), the SOCv isset up to the BMS SOC (S408), and if the low current state is notmaintained (S407), the SOCi is set up to the BMS SOC (S409). The SOC ofa battery in the battery management system is calculated through theabove mentioned process (S410). Hereinafter, each step in the BMS SOCmeasuring method will be described in detail.

A. First Step: Collection of Current Data, Voltage Data, TemperatureData and the Like

This step collects the current data, voltage data and the like from theBMS. In this step, the current data may be not measured precisely due totrouble of a current sensor. Particularly, in case that the currentsensor does not measure precisely the current intensity, but measuresonly a rough value thereof, considerable error may occur in the currentestimating process. However, in the SOC measuring method of the presentinvention, the error of SOCi is compensated with the SOCv. It waschecked through an actual simulation whether the SOC measuring method ofthe invention exactly calculated the BMS SOC. As a result, since theerror was gradually accumulated in the SOCi, but compensated with theSOCv, there was no problem in calculating the final BMS SOC. It wasconfirmed that an error between a calculated value and an actual valuewas within a target tolerance of 5.000% that was 1.502˜−4.170%. That is,although the current was inaccurately measured due to the trouble of thecurrent sensor, there was not a large error in the SOC measuring methodof the invention. Besides the trouble of the current sensor, otherproblems may occur. The current value may be offset owing to the troubleof the current sensor or trouble of CAN (controller Area Network), andthen transferred.

FIG. 5 is a graph shown a result of simulation in a case that offset of1A occurs in accordance with an embodiment of the present invention. Asshown in FIG. 5, the error is accumulated in the SOCi. It is understoodthat the degree of accumulation is very large. The accumulation iscaused by that 1A is offset and calculated. However, it is alsounderstood that the SOCv compensation occurs appropriately and thus theerror does not occur considerably.

According to the whole analysis, since the SOCv compensation does notoccur at beginning and end parts of a pattern, in which charging anddischarging operations occur, there may be generated a problem in theBMS SOC. However, if the SOCv compensation occurs after the charging anddischarging operations, it is possible to secure reliability of thecalculation. Also, in case that offset of −1A occurs, it is possible tosecure the reliability thereof in the same way.

B. Second Step: Calculation of SOCi Through Current Accumulation

In this step, the current data collected in the first step isaccumulated and then added to the SOC calculated in the previous timeinterval, thereby calculating the SOCi. The calculation is carried outby integrating the current over time. A calculated result is divided bya whole capacity, and then the rest capacity is expressed in percentage.This may be expressed by an equation 1 as followed:

$\begin{matrix}{{{{SOC}(\%)} = {\frac{{Remaining}\mspace{14mu} {Capacity}\mspace{14mu} ({Ah})}{{Nominal}\mspace{14mu} {Capacity}\mspace{14mu} ({Ah})} \cdot 100}}{{SOC}_{i} = {\frac{\int{i{t}}}{{Ah}_{nominal}} \cdot 100}}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In the SOC measuring method of the present invention, since the currentis detected every second, the equation 1 may be expressed by an equation2

$\begin{matrix}{{{SOC}_{i}(k)} = {{{SOC}\left( {k - 1} \right)} + {\frac{1}{Q_{\max}} \cdot {I(k)} \cdot t}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

That is, the calculation of SOCi in a step k is performed byaccumulating the increased SOC to the SOC in a step k−1. The increasedSOC is the current flowed in step k, multiplied by interval time t, anddivided by the whole capacity Qmax.

C. Third Step: Low Pass Filtering

The current data and the voltage data collected in the first step arepassed through a low pass filter. The present invention employs a thirdorder low pass filter, and a filter constant f is 0.6. However, thepresent invention is not limited to the conditions, and may use otherkind of filters and other filter constants. The filter used in thepresent invention may be expressed in the form of an equation 3 asfollows:

gi(n)=f ² i+3(1−f)gi(n−1)+3(1−f)² gi(n−2)+(1−f)³ gi(n−3)  Equation 3

In the SOC measuring method of the present invention, there are totalsix kinds of current data and voltage data that are needed in anequivalent circuit model. The current data is used as it is, and thevoltage data uses a difference value from an initial value. A currentvalue, a differential value of the current and a second differentialvalue of the current form one set of the current data. A differencevalue between an initial voltage value and a present voltage value, afirst differential value thereof and a second differential value thereofform one set of the voltage data. Reasons why the differential data isrequired and the difference value of voltage is required will be fullydescribed in the description of the equivalent circuit model.

D. Fourth Step: Equivalent Circuit Model and Adaptive Digital Filtering

The equivalent circuit model may be embodied into two models accordingto the embodiments of the present invention. In other words, theequivalent circuit model may be embodied into a first equivalent circuitmodel and a second equivalent circuit model according to each embodimentof the present invention. Hereinafter, the first equivalent circuitmodel will be described with reference to FIGS. 6 to 8, and the secondequivalent circuit model will be described with reference to FIG. 9.

1) First Equivalent Circuit Model

(1) First Equivalent Circuit Model

In this step, the current data and the voltage data collected in thethird step are applied to a battery model so as to obtain the OCV (opencircuit voltage). This is caused by that it is possible to obtain theSOCv through the OCV. As the battery model, there is a first-principlemodel that considers thermal behavior and electrochemical phenomenon ina battery. However, since excessive time and cost are required todevelop the above-mentioned model, the battery model in the presentinvention is embodied by an equivalent circuit model which is simplyexpressed by an electric circuit.

A modeling object is a lithium polymer battery (LiPB), and a circuitmodel is comprised of a first model. FIG. 6 is a view showing anequivalent circuit model in accordance with an embodiment of the presentinvention. The SOC measuring method of the present invention uses theequivalent circuit model that is expressed by a simple electric circuit.Each element such as a resistor and a capacitor included in theequivalent circuit model has a meaning shown in Table 1 as follows:

TABLE 1 Element of equivalent circuit model Step Process I Current(charge: (+)/discharge (−)) V Terminal voltage V_(o) Open circuitvoltage (OCV) R₁ Lumped interfacial resistances R₂ Lumped seriesresistances C Electric double layer capacitor

In FIG. 6, R₂ is resistance in electrodes, and R₁ and C are resistanceand a capacitor that express an electric double layer generated at aninterface between one electrode and the other electrode or a separator.Typically, a numerical value of each parameter is obtained through thefirst-principle model or an experiment. The equivalent circuit model ofFIG. 6 may be expressed by an equation 4 as follows:

$\begin{matrix}{{\Delta \; V} = {{\Delta \; V_{0}} + {\left( \frac{R_{1} + R_{2} + {{CR}_{1}R_{2}s}}{1 + {{CR}_{1}s}} \right)I}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

In the equation 4, it can be understood that the OCV is obtained byobtaining the parameters corresponding to each element forming theequivalent circuit model. In other words, an object of the batterymodeling according to the present invention is to obtain the OCV byobtaining each parameter and substituting the obtained parameter in theequation 4.

The equation 4 may be derived through a process as follows. In theequivalent circuit model of FIG. 6, the current may be expressed in theform of an equation 5 by virtue of Kirchhoff's law.

I+I ₂ +I ₃=0  Equation 5

Further, when a model is set up in consideration of values of theresistance and the capacitor in the entire circuit, it may be expressedby an equation 6.

$\begin{matrix}{{V = {V_{0} + {IR}_{2} - {I_{3}R_{1}}}}{V = {V_{0} + {IR}_{2} - \frac{Q}{C}}}{I_{2} = \frac{Q}{t}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

Herein, when the voltage and the OCV are expressed by difference from aninitial value (t=0), it may be expressed by an equation 7.

ΔV=V(t)−V(0)

ΔV ₀ =V ₀(t)−V ₀(0)  Equation 7

If the equation 7 is arranged in consideration of ΔV₀=V₀(t)−V₀(0), itmay be expressed by an equation 8.

$\begin{matrix}{{{\Delta \; V} = {{\Delta \; V_{0}} + {IR}_{2} - {I_{3}R_{1}}}}{{\Delta \; V} = {{\Delta \; V_{0}} + {IR}_{2} - \frac{Q}{C}}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

If the equation 8 is differentiated over time and then arranged, it maybe expressed by an equation 9.

$\begin{matrix}{{\frac{\left( {{\Delta \; V} - {\Delta \; V_{0}}} \right)}{t} + {\frac{1}{{CR}_{1}}\left( {{\Delta \; V} - {\Delta \; V_{0}}} \right)}} = {{\frac{R_{2}}{{CR}_{1}}I} + {R_{2}\frac{I}{l}} + \frac{I}{C}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

Then, if it is converted using Laplace transform, it may be expressed byan equation 10.

$\begin{matrix}{{\Delta \; V} = {{\Delta \; V_{0}} + {\left( \frac{R_{1} + R_{2} + {{CR}_{1}R_{2}s}}{1 + {{CR}_{1}s}} \right)I}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

Herein, assuming that the quantity of change in the current isproportional to the quantity of change in the OCV, and a proportionalconstant is h, the following equation may be set up:

${\Delta \; V_{0}} = {\frac{h}{s}I}$

If the equation is substituted in the equation 10, it may be expressedby an equation 11

$\begin{matrix}{{\Delta \; V} = {\frac{{\left( {R_{1} + R_{2}} \right)s} + {{CR}_{1}{hs}} + h + {{CR}_{1}R_{2}s^{2}}}{\left( {1 + {{CR}_{1}s}} \right)s}I}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Herein, each factor may be defined by an equation 12.

ΔV=V₁ I=I₁

sΔV=V₂ sI=I₂

s²ΔV=V₂ s²I=I₃  Equation 12

If the defined factors are is substituted in the equation 11, it may beexpressed by an equation 13

V ₂ =−CR ₁ V ₃ +CR ₁ R ₂ I ₃+(R ₁ +R ₂ +CR ₁ h)I ₂ +hI ₁  Equation 13

If the equation 13 is expressed in the form of a matrix, it may beexpressed by an equation 14

$\begin{matrix}{V_{2} = {\begin{bmatrix}V_{3} & I_{3} & I_{2} & I_{1}\end{bmatrix}\begin{bmatrix}{- {CR}_{1}} \\{{CR}_{1}R_{2}} \\{R_{1} + R_{2} + {{CR}_{1}h}} \\h\end{bmatrix}}} & {{Equation}\mspace{14mu} 14}\end{matrix}$

Herein, factors relevant to the current and voltage may be obtainedthrough the current data and voltage data that are collected from theBMS and filtered in the third step. Each parameter R₁, R₂, C, h isobtained by substituting the obtained factors and using the adaptivedigital filter. A method of using the adaptive digital filter will bedescribed later. If the parameters related to each situation areobtained through the filter, they are substituted in an equation 15 thatis a basic equation for calculating the OCV.

$\begin{matrix}{{{{\Delta \; V_{0}} + {{CR}_{1}s\; \Delta \; V_{0}}} = {V_{1} + {{CR}_{1}V_{2}} - {{CR}_{1}R_{2}I_{2}} - {\left( {R_{1} + R_{2}} \right)I_{1}}}}{{\Delta \; V_{0}} = \frac{V_{1} + {{CR}_{1}V_{2}} - {{CR}_{1}R_{2}I_{2}} - {\left( {R_{1} + R_{2}} \right)I_{1}}}{1 + {{CR}_{1}s}}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

The OCV obtained by using the equation 15 is used for calculating theSOCv in a next step.

The SOC measuring method of the present invention uses theabove-mentioned equivalent circuit model. However, if an equationderived from the model is further integrated by one step, an equation 16may be obtained.

$\begin{matrix}{{\Delta \; V} = {\frac{{{CR}_{1}R_{2}s} + \left( {R_{1} + R_{2}} \right) + {h/s} + {{CR}_{1}h}}{{{CR}_{1}s} + 1}I}} & {{Equation}\mspace{14mu} 16}\end{matrix}$

By dividing a denominator and a numerator of the original equation by s,it is possible to obtain integration effect. FIG. 7 shows actual SOC andcalculated BMS SOC in case of using a model providing the integrationeffect, and FIG. 8 is a graph showing a compensation point in case ofusing the model providing the integration effect.

In case of using the equivalent circuit model of the present invention,the compensation occurs properly as a whole. If the model providing theintegration effect is used, the compensation occurs further frequently.Also if the model providing the integration effect is used, noise isfurther generated, particularly, at a potion that the compensationoccurs. This means that the data becomes unstable as a whole, whencarrying out the integration. However, since the degree of unstable datais not high, it is possible to use the model providing the integrationeffect. Basically, it is the most preferable to use the equivalentcircuit model of the present invention, but if necessary, the modelproviding the integration effect may be used.

(2) Adaptive Digital Filter

Like the equation 14, the equivalent circuit model may be expressed inthe form of a matrix. In the equation 14, assuming that

$\quad\begin{bmatrix}V_{3} \\I_{3} \\I_{2} \\I_{1}\end{bmatrix}$

is w, and

$\quad\begin{bmatrix}{- {CR}_{1}} \\{{CR}_{1}R_{2}} \\{R_{1} + R_{2} + {{CR}_{1}h}} \\h\end{bmatrix}$

is θ, the equation 14 may be expressed by an equation 17.

V₂=w⁻¹θ  Equation 17

In this matrix, w obtains through the third step in which the currentdata and the voltage data are passed through the low pass filter, and V₂also obtains through the same result. An object of the adaptive digitalfilter is to obtain the matrix θ through the two values and estimate theparameter values in real time through each element. Assuming that V₂passing through the low pass filter is gV₂, the equation 17 may beexpressed by an equation 18.

gV₂=w⁻¹θ  Equation 18

First of all, an initial value of the matrix θ is obtained by obtainingthe parameter values in an initial state in which the current is notflowed and the voltage has an OCV value and then substituting theparameter values in the equation 18. A matrix at this time is indicatedby θ_(o). A square of the matrix is expressed by an equation 19.

P₀=θ₀ ²  Equation 19

Herein, a matrix K required to continuously renew the matrix θ may bedefined as an equation 20.

$\begin{matrix}{K = \frac{P_{0} \cdot w}{R + {w^{- 1} \cdot P_{0} \cdot w}}} & {{Equation}\mspace{14mu} 20}\end{matrix}$

wherein R is a value that is decided so as to prevent a denominator frombeing diverged to 0 by an initial value of gV₂, and the value is verysmall. The matrix may be arranged to an equation 21.

$\begin{matrix}{K = {\frac{P_{0} \cdot w}{R + {w^{- 1} \cdot P_{0} \cdot w}} = \frac{{{gV}_{2}\left( {n - 1} \right)} \cdot \theta_{0}}{R + \left\{ {{gV}_{2}\left( {n - 1} \right)} \right\}^{2}}}} & {{Equation}\mspace{14mu} 21}\end{matrix}$

wherein gV₂(n−1) is a just previous value of gV₂. The continuous renewalof the matrix θ is occurred by proportional relationship like anequation 22.

$\begin{matrix}{\frac{\theta}{{gV}_{2}(n)} = \frac{\theta_{0}}{{gV}_{2}\left( {n - 1} \right)}} & {{Equation}\mspace{14mu} 22}\end{matrix}$

The equation 22 may be arranged into an equation 23.

$\begin{matrix}{\theta = {\theta_{0} - \left\lbrack {\frac{{{gV}_{2}\left( {n - 1} \right)} \cdot \theta_{0}}{\left\{ {{gV}_{2}\left( {n - 1} \right)} \right\}^{2}} \cdot \left\{ {{{gV}_{2}\left( {n - 1} \right)} - {{gV}_{2}(n)}} \right\}} \right\rbrack}} & {{Equation}\mspace{14mu} 23}\end{matrix}$

Since R is very small, the matrix K may be substituted. This is arrangedinto an equation 24.

θ=θ₀ −[K·{gV ₂(n−1)−gV ₂(n)}]  Equation 24

If a relational expression is substituted in the equation 24, it may beexpressed by an equation 25

θ=θ₀ −[K·{w ⁻¹·θ₀ −gV ₂(n)}]  Equation 25

A value of θ in the equation 25 may be calculated through the currentdata, the voltage data and the previous matrix θ. Therefore, it ispossible to continuously estimate each parameter. After the initialstage, the matrix θ and the matrix P are renewed with new calculatedvalues. Then, the OCV is calculated through the obtained parameters.

2) Second Equivalent Circuit Model

(1) Second Equivalent Circuit Model

Hereinafter, a second equivalent circuit model and an adaptive digitalfiltering method in accordance with a second embodiment of the presentinvention will be described with reference to FIG. 9.

The second equivalent circuit model and the adaptive digital filteringmethod in accordance with the second embodiment of the present inventionprovides a discrete equivalent circuit modeling method by usingcharacteristic that the BMS discretely receives a voltage value, acurrent value and a temperature value of a battery. The secondequivalent circuit model according to the second embodiment of thepresent invention, which is a kind of a reduced model, simply expresseselectrochemical characteristic in the battery. Therefore, since it ispossible to easily design a model and also to minimize a time periodrequired for a modeling operation, it is adaptively applied to the BMS.

FIG. 9 is a view showing an equivalent circuit model in accordance withanother embodiment of the present invention.

The second equivalent circuit model according to the second embodimentof the present invention is provided as a primary model. Each elementsuch as resistance, capacitor and the like of the model has its ownmeaning shown in Table 1 as follows:

TABLE 2 Element of equivalent circuit model Step Process I Current(charge: (+)/discharge (−)) V Terminal voltage V_(o) Open circuitvoltage (OCV) R₀ Lumped interfacial resistances R Lumped seriesresistances C Electric double layer capacitor

In FIG. 9, as shown in Table 2, R₀ is resistance in electrodes, and Rand C are resistance and a capacitor that express an electric doublelayer generated at an interface between one electrode and the otherelectrode or a separator, and V0 is the OCV of the battery.

A core idea applied in the second equivalent circuit model is that thecurrent data and the voltage data are discretely input to the BMS atregular time intervals. Due to such core idea, it is possible to embodythe model that expresses the behavior of the battery through the secondequivalent circuit model. The parameters used in the model arecalculated by the adaptive digital filter.

Equations 26 to 29 are provided through FIG. 9 and Table 2.

$\begin{matrix}{{I + I_{2} + I_{3}} = 0} & {{Equation}\mspace{14mu} 26} \\{V = {V_{0} + {IR}_{0} - {I_{3}R}}} & {{Equation}\mspace{14mu} 27} \\{V = {V_{0} + {IR}_{0} - \frac{Q}{C}}} & {{Equation}\mspace{14mu} 28} \\{I_{2} = \frac{Q}{t}} & {{Equation}\mspace{14mu} 29}\end{matrix}$

An equation 30 is provided by integrating the equation 28 over time andthen arranging it.

$\begin{matrix}{{{\frac{}{t}\left( {V - V_{0}} \right)} + {\frac{1}{RC}\left( {V - V_{0}} \right)}} = {{\frac{I}{C}\left( {1 + \frac{R_{0}}{R}} \right)} + {R_{0}\frac{I}{t}}}} & {{Equation}\mspace{14mu} 30}\end{matrix}$

An equation 31 is provided by differentiating the equation 30 over timeusing an integrating factor.

$\begin{matrix}{V = {{\frac{Q(0)}{C}^{{- t}/{RC}}} + V_{0} + {IR}_{0} + {\frac{1}{C}{\int_{\xi = 0}^{\xi = t}{\left( {{I(\xi)}^{{--{({t - \xi})}}/{RC}}} \right){\xi}}}}}} & {{Equation}\mspace{14mu} 31}\end{matrix}$

Assuming that a polarization phenomenon in the battery does not occur atan initial time of the BMS operation, Q(0)=0. Therefore, the equation 31may be expressed by an equation 32.

$\begin{matrix}{V = {V_{0} + {IR}_{0} + {\frac{I}{C}{\int_{\xi = 0}^{\xi = t}{\left( {{I(\xi)}^{{--{({t - \xi})}}/{RC}}}\  \right){\xi}}}}}} & {{Equation}\mspace{14mu} 32}\end{matrix}$

In the equation 32, since the current data and the voltage data areinput to the BMS at regular time intervals, it is possible to discretelyexpress it A data input time interval is Δt.

In case of t≦0, assuming that I(t)=0 and T=0, it may be expressed asfollows

∫₀ ⁰(I(ξ)e ^(−(t−ξ)IRC)) dξ=0,

Therefore, the equation 32 may be expressed by an equation 33

V−V ₀ −IR ₀|_(t=0)=0  Equation 33

Further, in case that t=Δt=t1, i.e., a period of time has passed by Δt,the equation 32 may be expressed into an equation 34 through partialintegration.

$\begin{matrix}{{{V - V_{0} - {IR}_{0}}}_{t = t_{1}} \approx {\frac{^{{- t_{1}}/{RC}}}{C}\left( {{I\left( t_{1} \right)}\Delta \; {t \cdot ^{t_{1}/{RC}}}} \right)}} & {{Equation}\mspace{14mu} 34}\end{matrix}$

Furthermore, in case that t=2Δt=t2, i.e., a period of time has passedfrom t1 to Δt, the equation 32 may be expressed into an equation 35through partial integration.

$\begin{matrix}{{{V - V_{0} - {IR}_{0}}}_{t = t_{2}} \approx {\frac{^{{- t_{2}}/{RC}}}{C}\left\lbrack {\left( {{I\left( t_{2} \right)}\Delta \; {t \cdot ^{t_{2}/{RC}}}} \right) + \left( {{I\left( t_{1} \right)}\Delta \; {t \cdot ^{t_{1}/{RC}}}} \right)} \right\rbrack}} & {{Equation}\mspace{14mu} 35}\end{matrix}$

The equations 34 and 35 may be combined into an equation 36.

$\begin{matrix}\left. {{{V - V_{0} - {IR}_{0}}}_{t = t_{2}} \approx {\frac{{I\left( t_{2} \right)}\Delta \; t}{C} + {^{{- \Delta}\; {t/{RC}}}\left\lbrack {V - V_{0} - {IR}_{0}} \right.}_{t = t_{1}}}} \right\rbrack & {{Equation}\mspace{14mu} 36}\end{matrix}$

By repeating the above calculations, the equation 32 may be expressedinto an equation 37 with respect to a time period t.

$\begin{matrix}\left. {{{V - V_{0} - {IR}_{0}}}_{t} \approx {\frac{I\; \Delta \; t}{C} + {^{{- \Delta}\; {t/{RC}}}\left\lbrack {V - V_{0} - {IR}_{0}} \right.}_{t - {\Delta \; t}}}} \right\rbrack & {{Equation}\mspace{14mu} 37}\end{matrix}$

Therefore, the equivalent circuit model is calculated through theequation 38.

$\begin{matrix}\left. {V = {V_{0} + {IR}_{0} + {\frac{1}{C}I\; \Delta \; t} + {^{{- \Delta}\; {t/{RC}}}\left\lbrack {V - V_{0} - {IR}_{0}} \right.}_{t - {\Delta \; t}}}} \right\rbrack & {{Equation}\mspace{14mu} 38}\end{matrix}$

In the equation 38, Δt is a data input time interval, and t−Δt is aparameter value in the previous time interval. Assuming that α=1/C andβ=1/RC, the equation 38 may be simply arranged into an equation 39.

V=V ₀ +IR ₀ +αIΔt+exp(−βΔt)[V−V ₀ −IR ₀ |t−Δt]  Equation 39

In the equation 39, β is a time constant, and τ is a reciprocal numberand indicates a time when the battery arrives at a normal state.Generally, in case that a battery operation time of 3τ or more passes,it is estimated that the reaction in the battery arrives at the normalstate. The factors of current and voltage are collected from the BMS andthen calculated through the filtered current and voltage data. And theVOC is calculated by substituting each parameter.

R0 that indicates ohmic resistance of the battery itself decides a fixedvalue according to property of a material in the battery. Generally, thevalue is easily obtained through impedence. Variables α and β which arecombined with the parameters R and C related to polarization areoptimized through the adaptive digital filter.

(2) Adaptive Digital Filter

The equation 39 that mathematically indicates the equivalent circuitmodel of FIG. 9 may be expressed by an equation 40 as a determinant.

$\begin{matrix}{V = {\begin{bmatrix}V_{0} & {IR}_{0} & I & {{V - V_{0} - {IR}_{0}}}_{n - 1}\end{bmatrix}\begin{bmatrix}1 \\1 \\{{\alpha\Delta}\; t} \\{\exp \left( {{- {\beta\Delta}}\; t} \right)}\end{bmatrix}}} & {{Equation}\mspace{14mu} 40}\end{matrix}$

In the equation 40,

in case of

${\begin{bmatrix}V_{0} \\{IR}_{0} \\I \\{{V - V_{0} - {IR}_{0}}}_{n - 1}\end{bmatrix} = {{w\mspace{14mu}\begin{bmatrix}1 \\1 \\{{\alpha\Delta}\; t} \\{\exp \left( {{- {\beta\Delta}}\; t} \right)}\end{bmatrix}} = \theta}},$

the equation 40 may be expressed into an equation 41.

V=w^(T)θ  Equation 41

In the equation 41, w is calculated through the current data and thevoltage data, and v is also calculated through the current data and thevoltage data. The adaptive digital filter calculates θ through the twovalues w and V, and the parameter value is estimated through eachcomponent of θ in real time.

Assuming that V passed through the low pass filter is gV, the equation41 may be expressed into an equation 42.

gV=w^(T)θ  Equation 42

An initial value of θ is obtained by calculating a parameter in a statethat t=0, i.e., the current is not flowed and the voltage has an OCVvalue. A matrix at this time is θ₀.

θ₀ by θ₀ is equal to an equation 43.

P ₀=θ₀·θ₀ ^(T)  Equation 43

In the equation 43, a matrix k that is needed to continuously renew θmay be defined as an equation 44.

$\begin{matrix}{K = \frac{P_{0} \cdot w}{r + {w^{T} \cdot P_{0} \cdot w}}} & {{Equation}\mspace{14mu} 44}\end{matrix}$

In the equation 44, r is a constant that is defined to prevent adenominator from being diverged by V, and typically has a small value.The equation 44 may be changed into an equation 45 by arranging a matrixthereof.

$\begin{matrix}{K = {\frac{P_{0} \cdot w}{r + {w^{T} \cdot P_{0} \cdot w}} = \frac{{{gV}\left( {n - 1} \right)} \cdot \theta_{0}}{r + \left\{ {{gV}\left( {n - 1} \right)} \right\}^{2}}}} & {{Equation}\mspace{14mu} 45}\end{matrix}$

In the equation 45, gV(n−1) is a just previous value of gV. Assumingthat the continuous renewal of θ is occurred by proportionalrelationship of the equation 46, the equation 46 may be arranged into anequation 47.

$\begin{matrix}{\theta = {\theta_{0} - \left\lbrack {\frac{{{gV}\left( {n - 1} \right)} \cdot \theta_{0}}{\left\{ {{gV}\left( {n - 1} \right)} \right\}^{2}} \cdot \left\{ {{{gV}\left( {n - 1} \right)} - {{gV}(n)}} \right\}} \right\rbrack}} & {{Equation}\mspace{14mu} 47}\end{matrix}$

In the equation 47, since r is a very small value, it may be substitutedby K. That is, the equations 45 and 47 may be combined into an equation48.

θ=θ₀ −[K·{gV(n−1)−gV(n)}]  Equation 48

By instituting the equation 42 to the equation 48, it is possible toobtain an equation 49.

θ=θ₀ −[K·{w ^(T)·θ₀ −gV(n)}]  Equation 49

Main variables in the equation 49 are obtained through the current data,the voltage data and θ₀. Therefore, each parameter is continuouslyestimated in the same manner.

Further, after the initial stage, θ and P may be renewed into newvalues. Thus, the parameter values suitable to the equivalent circuitmodel may be continuously renewed. Also, it is possible to calculate theOCV using the parameters obtained in the same way.

E. Fifth Step: Calculation of SOCv Through Open Circuit Voltage andTemperature

A value of the OCV is calculated through the equivalent circuit modelaccording to the present invention. Generally, SOCv is influenced by theOCV and the temperature and thus expressed by a function between them.In a room temperature, relation between OCV and SOCv is equal to anequation 50.

SOC _(v)(n)=−539.069·V ₀(n)⁴+7928.96·V ₀(n)³−43513.3·V ₀(n)²+105698·V₀(n)−95954.8  Equation 50

As described above, it is possible to obtain SOCv through the relationbetween OCV and SOCv and the value of OCV at the room temperature.However, there is a problem in the equation 50. Since it is a model atthe room temperature, errors occur when the temperature is changed. Amaximum value and a minimum value of the error generated when asimulation is performed at a temperature of 45˜−10° C. besides a roomtemperature of 25° C. are described in Table 3.

TABLE 3 Maximum and minimum error of each temperature simulation Error(%) Temperature Max Min 25° C. 0.714 −1.936 45° C. 0.008 −2.692 −10° C. 0.000 −8.542

Therefore, using the relation between SOCv and OCV at the roomtemperature, it is possible to obtain precise values at a temperature of45° C. However, it is understood that the values are incorrect at atemperature of −10° C. In other words, at the temperature of −10° C., itis necessary to use other relation or introduce a factor that considersthe temperature. First of all, the relation between SOCv and OCV at thetemperature of −10° C. is expressed by an equation 51.

SOC _(v)(n)=−425.6·V ₀(n)⁴+6207·V ₀(n)³−33740·V ₀(n)²+81113·V₀(n)−72826  Equation 51

F. Sixth Step: Proper Selection of SOC

In the sixth step, it is decided which one is selected from SOCi andSOCv obtained in the previous step. In case of the low current state, itis known that SOCv has an exact value. Therefore, SOCv is used in thelow current state. And the calculation is performed by accumulating thecurrent value to the just previous SOC in other states.

In criteria of judgment of the low current state, if the current havinga desired absolute value or less is continuously flowed for a desiredperiod of time, it is determined as the low current state. Herein, theabsolute value of current and the current flowing time are importantcriteria. Preferably, the absolute value and the time are 2A and 20˜60s,respectively.

In case that the absolute value of current intensity is more than 2A,the criteria of judgment of the low current state is relaxedconsiderably, and it is judged as a state that the current is beingflowed even at a section that the current is not flowed. As a result, itis difficult to precisely estimate SOCv, and thus SOCv compensation iscarried out too frequently. However, in case that the absolute value ofcurrent is less than 2A, it is impossible to recognize the low currentwhen offset occurs. Therefore, it is preferable to set up the criteriato 2A.

It is more complicated to judge the criteria of current flowing time.Assuming that a period of time when the current corresponding to batterycharging or discharging and having an intensity of 2A or less iscontinuously flowed is t, the criteria may be expressed as in Table 4.

TABLE 4 Time scale criteria for SOCv compensation Continuous timecriteria Judgment t < a Use of SOCi a ≦ t < b Compensation with SOCv atthe moment that low current section is ended b ≦ t SOCv compensation ata point of time of b seconds

FIG. 10 shows the time criteria. Referring to FIG. 10, if the lowcurrent is flowed for 20 seconds or less, SOC is calculated by thecurrent accumulation. However, if the low current is flowed for 20seconds or more, the SOCv compensation occurs. The SOCv compensation iscarried out at a point of time when the low current section having anintensity of 2A or less is finished. However, if the low current isflowed for 60 seconds or more, the SOCv compensation is carried out at apoint of time of 60 seconds. And at a moment that the compensationoccurs, the continuous period of time when the low current is flowed iscalculated again.

The criteria are decided by selecting the optimal time criteria fromvarious simulations. The time criteria of minimum 20 seconds is decidedbased on a fact that the compensation is occurred even if the currentsensor has a trouble. Actually, in case that the time criteria ischanged into 10 seconds, an error of 8.3% occurs. Further, in case thatthe continuous period of time is set up to 60, the compensation does notoccur properly at an up/down pattern, and the error is accumulated.

The main cause of allowing the time criteria to be movable is to preventincrease of the error due to improper compensation after the batterycharging for a long time period. The present invention is not limited tothe time criteria, and may include various time criteria.

FIG. 11( a) shows an error in case of performing a simulation with atime criteria of 20 seconds, and FIG. 11( b) shows an error in case ofperforming the simulation with a proposed time criteria.

Referring to FIG. 11, the utility of the proposed time criteria will beunderstood. In case of the simulation with a time criteria of 20seconds, it was understood that considerable error occurred at beginningand end portions that are just after the charging. However, in case ofthe simulation with the proposed time criteria, the error did not occurat beginning and end portions. Entire error magnitude is hardly changed,but the error occurred at a point of time when the charging is finishedis reduced by 1.5% or more.

The proposed time criteria is more effective in a low temperature state.In case of the low temperature state, it is generally effective, ofcause, at the point of time when the charging is finished. In case ofusing the proposed time criteria, a maximum value of the error isreduced from 7,287% to 3.542%, and a minimum value thereof is reducedfrom −4.191% to −3.870%. This means that the proposed time criteria ismore effective in a low temperature state.

If it is judged as the low current state on the basis of the time andcurrent criteria as mentioned above, SOCv is set up to SOC. Otherwise,BMS SOC is precisely calculated by using the SOC measuring method of thepresent invention.

While the present invention has been described with respect to thespecific embodiments, it will be apparent to those skilled in the artthat various changes and modifications may be made without departingfrom the spirit and scope of the invention as defined in the followingclaims.

INDUSTRIAL APPLICABILITY

The SOC measuring method of the present invention may be embodied in theform of a program that is executed through various computing means, andthen recorded on a computer-readable medium. The computer-readablemedium may include a program order, a data file, a data structure andthe like, or any combination thereof. The program order recorded on themedium may be specially designed or constructed to be used in thepresent invention, or used in a state that is provided to those skilledin the field of computer software. Further, the computer-readable mediummay include a magnetic media such as a hard disk, a floppy disk and amagnetic tape, an optical media like DVD, a magnetro-optical media likea floptical disk, and a hardware device for storing and executing aprogram order, such as ROM, RAM and a flash memory. The medium may be atransmission media of a wave guide, a metal wire or light including acarrier wave for transmitting a signal indicating a program order, adata structure and the like. The program order includes a machinelanguage code formed by a compiler as well as a high level language codethat is formed using an interpreter so as to be executed by a computer.In order to perform an operation of the present invention, the hardwaredevice may be constructed to be operated by one or more softwaremodules, and the reverse thereof is the same.

1. A method for measuring SOC of a battery, comprising: obtaining current data, voltage data and temperature data by measuring current, voltage and temperature of the battery; calculating SOCi (State Of Charge based on current) by accumulating the current data; calculating OCV (Open Circuit Voltage) using an equivalent circuit model in which the current data, the voltage data and the battery are simply expressed by an electric circuit; calculating SOCv (State Of Charge based on voltage) using the temperature data and the OCV; and judging a current state of the battery for a desired period of time, and setting up the SOC of the battery using at least one of the SOCv and the SOCi.
 2. The method of claim 1, wherein the calculating of OCV using an equivalent circuit model in which the current data, the voltage data and the battery are simply expressed by an electric circuit comprises: Filtering the current data and the voltage data using a low pass filter; Calculating a parameter used in the equivalent circuit model by applying the filtered current data and voltage data to the equivalent circuit model and an adaptive digital filter; and calculating the OCV using the parameter.
 3. The method of claim 2, wherein the low pass filter is a third order low pass filter.
 4. The method of claim 2, wherein the equivalent circuit model is expressed by an electric circuit using a resistance parameter R, a current parameter I, a capacitor parameter C, a terminal voltage parameter V and VOC parameter Vo.
 5. The method of claim 2, wherein a value of the parameter used in the equivalent circuit model is renewed by the adaptive digital filter.
 6. The method of claim 1, wherein the judging of the current state of the battery for the desired period of time, and setting of the SOC of the battery using at least one of the SOCv and the SOCi comprises: setting up the SOCv to the SOC of the battery, if the battery is in a low current state for the desired period of time; and setting up the SOCv to the SOC of the battery, if the battery is not in a low current state for the desired period of time.
 7. The method of claim 6, wherein the desired period of time is 20˜60 seconds, and the low current criteria is 2A.
 8. The method of claim 1, wherein the calculating of the OCV using the equivalent circuit model in which the current data, the voltage data and the battery are simply expressed by the electric circuit comprises calculating the OCV using an integration model of the equivalent circuit model in which the current data, the voltage data and the battery are simply expressed by the electric circuit.
 9. An apparatus for measuring SOC of a battery, comprising: a battery information obtaining part that measures current, voltage and temperature of the battery and obtains current data, voltage data and temperature data; a current accumulating part that calculates SOCi by accumulating the current data; a OCV calculating part that calculates OCV using an equivalent circuit model in which the current data, the voltage data and the battery are simply expressed by an electric circuit; a SOCv estimating part that estimates SOCv using the temperature data and the OCV; and a SOC setting part that judges a current state of the battery for a desired period of time, and sets up the SOC of the battery using at least one of the SOCv and the SOCi.
 10. The apparatus of claim 9, further comprising a low pass filtering part that filters the current data and the voltage data using a low pass filter, wherein the OCV calculating part applies the current data and the voltage data filtered by the low pass filtering part to the equivalent circuit model and an adaptive digital filter, calculates a parameter used in the equivalent circuit model and then calculates the OCV using the parameter.
 11. The apparatus of claim 10, wherein the low pass filter is a third order low pass filter.
 12. The apparatus of claim 10, wherein the equivalent circuit model is expressed by an electric circuit using a resistance parameter R, a current parameter I, a capacitor parameter C, a terminal voltage parameter V and VOC parameter Vo.
 13. The apparatus of claim 10, wherein the adaptive digital filter renews a value of the parameter using in the equivalent circuit model, continuously.
 14. The apparatus of claim 9, wherein the SOC setting part sets up the SOCv to the SOC of the battery, if the battery is in a low current state for the desired period of time, and also sets up the SOCi to the SOC of the battery in other case.
 15. The apparatus of claim 14, wherein the desired period of time is 2060 seconds, and the low current criteria is 2A.
 16. The apparatus of claim 9, wherein the OCV calculating part calculates the OCV through an integration model of the equivalent circuit model.
 17. A computer-readable recording medium which records a program for executing the method of claim
 1. 